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Search a target in a rotated sorted array with no duplicates. Modified binary search identifies which half is sorted, then checks the target range. O(log n) time.
Find the minimum element in a rotated sorted array with no duplicates. Binary search: the minimum is in the unsorted half. O(log n) time O(1) space.
Find the one duplicate in [1..n] without modifying the array using Floyd's tortoise-and-hare cycle detection.
Find a peak element in O(log n) by binary searching on the slope direction — always move toward the higher neighbor.
Find the median of two sorted arrays in O(log(min(m,n))) by binary searching for the correct partition point.
Minimize the largest sum among m subarrays by binary searching on the answer and greedy checking feasibility.
Find the longest substring that appears at least twice using binary search on length and Rabin-Karp rolling hash for O(n log n) average time.
Master every binary search pattern: classic, left/right boundary, rotated array, BS on answer, and 2D matrix — with templates and full index of 45 problems.
Implement classic binary search to find a target in a sorted array in O(log n) time.
Find the first bad version using left-boundary binary search: shrink hi to mid when version is bad.
Find where a target would be inserted in a sorted array using left-boundary binary search returning lo.
Compute integer square root using right-boundary binary search to find the largest k where k*k <= x.
Find the starting and ending positions of a target in a sorted array using two separate binary searches.
Search in a rotated sorted array by identifying which half is sorted and narrowing accordingly.
Find the minimum element in a rotated sorted array by comparing mid with right boundary to locate the rotation point.
Search a row-column sorted 2D matrix in O(log(m*n)) by treating it as a virtual 1D sorted array.
Find the minimum eating speed for Koko to finish all bananas in h hours using binary search on the answer space.
Find the minimum ship capacity to ship all packages within d days using binary search on capacity.
Find any peak element in O(log n) by always moving toward the uphill neighbor, which guarantees finding a peak.
Find the k closest elements to x in a sorted array by binary searching for the optimal left window boundary.
Find the single non-duplicate element in O(log n) by observing that pairs shift the parity of indices after the singleton.
Find the length of LIS in O(n log n) using patience sorting: binary search to maintain a sorted tails array.
Minimize the largest subarray sum when splitting into k parts using binary search on the possible answer range.
Search in a rotated sorted array that may contain duplicates by skipping lo++ when mid equals both boundaries.
Find the minimum day to make m bouquets of k adjacent flowers using binary search on the day value.
Find h-index from a sorted citations array in O(log n) using left-boundary binary search.
Count spell-potion pairs with product >= success by sorting potions and binary searching for each spell's threshold.
Find the kth smallest element in a row-column sorted matrix by binary searching on the value range.
Maximize the minimum distance between m balls in baskets using binary search on the answer (minimum distance).
Find the minimum in a rotated array with duplicates by shrinking hi-- when nums[mid]==nums[hi].
Find the median of two sorted arrays in O(log(min(m,n))) by binary searching for the correct partition point.
Count smaller elements to the right of each element using merge sort with position tracking in O(n log n).
Find the maximum number of nested envelopes by sorting by width ascending then height descending, then applying LIS.
Minimize the maximum value after performing k operations (average adjacent elements) using binary search on the answer.
Find the maximum length to cut k ribbons from given ribbons using binary search on the ribbon length.
Maximize nums[index] given array length n, sum constraint maxSum, and each element >= 1 using binary search on the peak value.
Find the kth missing number in a sorted array by binary searching on the number of missing elements up to each index.
Search a row-column sorted 2D matrix in O(m+n) using the staircase technique from top-right corner.
Place c cows in stalls to maximize the minimum distance between any two cows using binary search on the answer.
Count subarrays with sum in [lower, upper] using merge sort on prefix sums for O(n log n) complexity.
Find the picked number using binary search with the guess() API that returns -1, 0, or 1.
Count negatives in a sorted matrix in O(m+n) using the staircase approach or O(m log n) with binary search per row.
Check if a number is a perfect square in O(log n) using binary search or by exploiting odd-number sum identity.
Find the smallest letter in a circular sorted list that is greater than the target using left-boundary binary search.
Answer election queries for who is leading at time t by precomputing the leader at each vote and binary searching.
Find the duplicate in array of n+1 integers in [1,n] using binary search on value with count-of-smaller logic.
Find the kth smallest prime fraction from an array using binary search on the fraction value with a counting function.
Check if any element and its double both exist in an array using a hash set or sorting with binary search.
Implement get(key, timestamp) using binary search on stored sorted timestamps for O(log n) retrieval.
Maximize events attended by greedily attending the event with the earliest end date each day using binary search.
Find the kth smallest element from two sorted arrays in O(log(m+n)) using binary elimination of k/2 elements per step.
Find the minimum train speed to arrive on time given n rides (last ride doesn't wait) using binary search on speed.
Complete cheatsheet for Binary Search: all 7 patterns, the universal template, BS on answer guide, Big O reference, and MAANG priority.
Find path from top-left to bottom-right minimizing maximum absolute difference between consecutive cells. Use Dijkstra or binary search + BFS.
Implement weighted random selection by building a prefix sum array and using binary search to find the sampled index.
Design a time-stamped key-value store supporting set and get(key, timestamp) using binary search on sorted timestamps.
Find K closest elements to x in a sorted array using binary search to find the optimal left boundary.
Find the Kth smallest element in an n×n row-and-column sorted matrix using binary search on value range or heap.
Find minimum time to swim from top-left to bottom-right in a grid where time = max elevation on the path.
Find the nth number divisible by a, b, or c using binary search with inclusion-exclusion counting formula.
For each interval find the interval with the smallest start point >= the end point using sorted starts and binary search.
Count nodes in a complete binary tree in O(log^2 n) by comparing left and right heights to identify full subtrees.
Count nodes in complete binary tree in O(log^2 n) by comparing left vs right subtree heights recursively.
Find two numbers summing to target in a 1-indexed sorted array using inward two pointers in O(n) time O(1) space.
Find k closest integers to x in a sorted array using binary search to locate the optimal left boundary of the window.
Find the path from source to destination minimising the maximum edge weight. Binary search on the answer + BFS/DFS connectivity check. O(E log W) total.
Find the minimum time to swim from (0,0) to (n-1,n-1) where you can only move to a cell when time >= cell value. Two approaches: Dijkstra O(n² log n) and binary search + BFS O(n² log n).
Search for a target in a matrix where each row and column is sorted. O(m+n) solution using top-right corner elimination — a classic Google interview problem.
Find the median of two sorted arrays in O(log(min(m,n))) time using binary search on partition points. A classic hard problem testing deep binary search understanding.
Design a key-value store that returns values at or before a given timestamp. Uses a hashmap of sorted (timestamp, value) lists with binary search for O(log n) get.